Nonparametric Sequential Estimation of Zeros and Extrema of Regression Functions

摘要

Let (X,Y), (X sub 1, Y sub 1), (X sub 2, Y sub 2, ... be independent, identically distributed, bivariate random variables and let m(x)=E(Y/X=x) be the regression curve of y on X. This paper considers the estimation of zeros and extrema of the regression curve via stochastic approximation methods. The author presents consistency results of some sequential procedures and define termination rules providing fixed width confidence intervals for the parameters to be estimated. Keywords: kernel regression; nonparametric regression. (Author)